Problem: What do the following two equations represent? $x+y = 3$ $-5x-5y = -5$
Answer: Putting the first equation in $y = mx + b$ form gives: $x+y = 3$ $y = -x+3$ Putting the second equation in $y = mx + b$ form gives: $-5x-5y = -5$ $-5y = 5x-5$ $y = -1x + 1$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.